Pre-calc help? Factor f(x) = 4x^4 - 24x^3 + 35x^2 +6x -9?

Answer 1

Using rational root theorem, do synthetic division using 3 as a root:

3 | 4 .. -24 .. 35 .. 6 .. -9
........... 12 ..-36 ..-3 ... 9
--------------------------------
.... 4 .. -12 .. -1 ... 3 ... 0

The remaining cubic can be factored by grouping:

4x³ - 12x² - x + 3 =
4x²(x - 3) - 1(x - 3) =
(4x² - 1)(x - 3) =
(2x+1)(2x-1)(x-3)

so the complete factoring is
(2x+1)(2x-1)(x-3)²